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1.
This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained.  相似文献   

2.
This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.  相似文献   

3.
In this paper, the pth moment exponential stability for a class of impulsive stochastic functional differential equations with Markovian switching is investigated. Based on the Lyapunov function, Dynkin formula and Razumikhin technique with stochastic version as well as stochastic analysis theory, many new sufficient conditions are derived to ensure the pth moment exponential stability of the trivial solution. The obtained results show that stochastic functional differential equations with/without Markovian switching may be pth moment exponentially stabilized by impulses. Moreover, our results generalize and improve some results obtained in the literature. Finally, a numerical example and its simulations are given to illustrate the theoretical results.  相似文献   

4.
In this paper, the problem of mean-square integral input-to-state stability of nonlinear impulsive semi-Markov jump delay systems is investigated. By using stochastic Lyapunov functions together with Razumikhin technique, some sufficient conditions for mean-square integral input-to-state stability for a class of nonlinear impulsive semi-Markov jump delay systems are developed. In particular, the results obtained generalize and complement some recent literature. Finally, some numerical examples are given to show the effectiveness and advantages of the proposed techniques.  相似文献   

5.
In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results.  相似文献   

6.
In this paper, we investigate an eco-epidemic model with distributed time delay and impulsive control strategy. Firstly, by using Floquet theory of impulsive differential equation, we get the condition for the local stability of the prey eradication periodic solutions. Secondly, by means of impulsive equation compare theory, we get the condition for the global asymptotical stability of the prey eradication periodic solutions. Finally we study the permanence of the system. Numerical simulations (bifurcation diagram, the largest Lyapunov exponents and power spectra) are carried out to illustrate the above theoretical analysis and the rich dynamics phenomenon, which are caused by impulsive effects and time delay, for example bifurcation, double period solution, etc.  相似文献   

7.
In this paper, we consider the problem of mixed H∞ and passivity control for a class of stochastic nonlinear systems with aperiodic sampling. The system states are unavailable and the measurement is corrupted by noise. We introduce an impulsive observer-based controller, which makes the closed-loop system a stochastic hybrid system that consists of a stochastic nonlinear system and a stochastic impulsive differential system. A time-varying Lyapunov function approach is presented to determine the asymptotic stability of the corresponding closed-loop system in mean-square sense, and simultaneously guarantee a prescribed mixed H∞ and passivity performance. Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs). Finally, the effectiveness and applicability of the proposed method in practical systems are demonstrated by the simulation studies of a Chua’s circuit and a single-link flexible joint robot.  相似文献   

8.
In this letter, the existence and the global exponential stability of piecewise pseudo almost periodic solutions (PAPT) for bidirectional associative memory neural networks (BAMNNs) with time-varying delay in leakage (or forgetting) terms and impulsive are investigated by applying contraction mapping fixed point theorem, the exponential dichotomy of linear differential equations and differential inequality techniques. Furthermore, we give an explanatory example to illustrate the efficiency of the theoretical predictions.  相似文献   

9.
The topic of the paper is both the pth moment and almost sure stability on a general decay rate for neutral stochastic functional differential equations, by applying the Razumikhin approach. This concept is extended to neutral stochastic differential delay equations. The results obtained in the paper are more general and they may be specialized on the exponential, polynomial or logarithmic stability. Moreover, some neutral stochastic functional differential equations which are not pth moment or almost surely exponentially stable, could be stable with respect to a certain lower decay rate. In that sense, some nontrivial examples are presented to justify and illustrate the usefulness of the theory. More precisely, one can say anything about both the pth moment and almost sure exponential stability, although the solutions are pth moment and almost surely polynomially or logarithmically stable.  相似文献   

10.
This paper deals with the stability and dissipative problem of a class of stochastic hybrid system. The system under study involves Markovian jump, impulsive effects and time delay, which are often encountered in practice and are the sources of instability. Our attention is focused on analysis of whether the stochastic hybrid system with time-delay is stochastically asymptotically stable and strictly (Q, S, R) dissipative. By introducing an extra artificial time instance, the equivalent system is obtained and the sufficient conditions are derived by using linear matrix inequality (LMI) techniques. The main results of this paper unify the existing results on H∞ control.  相似文献   

11.
The problem of existence of almost periodic solutions of uncertain impulsive functional differential systems of fractional order is investigated. Using the Lyapunov method combined with the concept of uniformly positive definite matrix functions and Hamilton–Jacobi–Riccati inequalities new criteria are presented. The robust stability of the almost periodic solution is also discussed. We apply our results to an impulsive Lasota–Wazewska type model of fractional order. Our results extend the theory of almost periodic solutions for impulsive delay differential equations to the fractional-order case under uncertainty.  相似文献   

12.
This paper is concerned with the input-to-state stability (ISS) of impulsive stochastic systems. First, appropriate concepts of stochastic input-to-state stability (SISS) and pth moment input-to-state stability (p-ISS) for the mentioned systems are introduced. Then, we prove that impulsive stochastic systems possessing SISS-Lyapunov functions are uniformly SISS and p-ISS over a certain class of impulse sequences. As a byproduct, a criterion on the uniform global asymptotic stability in probability for the system in isolation (without inputs) is also derived. Finally, we provide a numerical example to illustrate our results.  相似文献   

13.
In this paper, by using Lyapunov functions, Razumikhin techniques and stochastic analysis approaches, the robust exponential stability of a class of uncertain impulsive stochastic neural networks with delayed impulses is investigated. The obtained results show that delayed impulses can make contribution to the stability of system. Compared with existing results on related problems, this work improves and complements ones from some works. Two examples are discussed to illustrate the effectiveness and the advantages of the results obtained.  相似文献   

14.
在现有文献的基础上，对一类马尔可夫调制的随机微分方程进行了研究，得到了其平凡解2阶均值指数稳定性和几乎必然指数稳定性的充分条件。对现有成果进行了改进。  相似文献   

15.
In this paper, on the basis of the theories and methods of ecology and ordinary differential equation, an ecological model consisting of two preys and one predator with impulsive control strategy and seasonal effects is established. Conditions which guarantee the global asymptotical stability of the prey-eradication periodic solution are obtained using the theory of impulsive equations, small amplitude perturbation skills, and comparison techniques. Further, the influences of the impulsive perturbation and seasonal effects on the inherent oscillation are studied numerically. These show to be consistent with the theoretical analysis and rich complex population dynamics, such as species extinction and permanence. Moreover, the population dynamical behavior of the model is demonstrated by the computed largest Lyapunov exponent. By investigating the strange attractors through their computed Fourier spectra, we know that seasonality has a profound effect on the population dynamical behavior. All these results are expected to be of use in the study of dynamic complexity of ecosystems.  相似文献   

16.
In this paper, a class of impulsive differential equations with Dirichlet boundary conditions are considered. Multiplicity results are obtained by critical point theory. Recent results in the literature are generalized and significantly improved.  相似文献   

17.
This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.  相似文献   

18.
In this paper, an adaptive feedback controller is designed to achieve complete synchronization of unidirectionally coupled delayed neural networks with stochastic perturbation. LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system. An example and numerical simulation are given to demonstrate the effectiveness of the theory results.  相似文献   

19.
This study addresses the exponential stability and positive stabilization problems of impulsive positive systems (IPSs) with time delay. Specially, three types of impulses, namely, disturbance, “neutral”, and stabilizing impulses, are considered. For each type of impulsive effect, the exponential stability criterion is established utilizing the Lyapunov–Razumikhin techniques. Moreover, on the basis of the obtained stability results, the state-feedback controller design problem is investigated to positively stabilize the IPSs with time delay under different types of impulsive effects. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.  相似文献   

20.
In this paper, we first deal with the robust stability of uncertain linear stochastic differential delay systems. The parameter uncertainties are time-varying and unknown but are norm-bounded via two types of uncertainties, and the delays are time invariant. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems. These results are given in terms of linear matrix inequalities. Two examples are presented to illustrate the effectiveness.  相似文献   

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